Comparative Finite Element Simulation of Nonlinear Vibrations and Sensor Output Voltage of Smart Piezolaminated Structures
Two geometrically nonlinear plate theories, based either on first- or third-order transverse shear deformation theory are used for finite element modeling and simulation of the transient response of smart structures incorporating piezoelectric layers. In particular the time histories of nonlinear vibrations and sensor voltage output of a thin beam with a piezoelectric patch bonded to the surface due to an applied step force are studied.
[1] E.F. Crawley, J. de Luis: Use of piezoelectric actuators as elements of
intelligent structures, AIAA Journal 25 (1987), 1373-1385.
[2] R. Lammering: The application of finite shell elements for composites
containing piezoelectric polymers in vibration control, Computers &
Structures 41 (1991), 1101-1109.
[3] H. Kioua, S. Mirza: Piezoelectric induced bending and twisting of
laminated composite shallow shells, Smart. Mater. Struct. 6 (2000), 476-
484.
[4] S. Lee, N.S. Goo, H.C. Park, K.J. Yoon, C. Cho: A nine-node assumed
strain shell element for analysis of a coupled electromechanical system,
Smart. Mater. Struct. 12 (2003), 355-336.
[5] Chr├│ścielewski, P. Klosowski, R. Schmidt: Theory and numerical
simulation of nonlinear vibration control of arches with piezoelectric
distributed actuators, Machine Dynamics Problems 20 (1998), 73-90.
[6] S. Yi, S.F. Ling, M. Ying: Large deformation finite element analyses of
composite structures integrated with piezoelectric sensors and actuators,
Finite Elements in Analysis and Design 35 (2000), 1-15.
[7] A. Mukherjee, A.S. Chaudhuri: Piezolaminated beams with large
deformations, Int. J. of Solids and Structures 14 (2002), 1567-1582.
[8] S. Lentzen, R. Schmidt: Simulation of sensor application and shape
control of piezoelectric structures at large deflections, in Advances in
Computational & Experimental Engineering & Science, eds. S.N. Atluri,
A.J.B Tadeu, p. 439-444, Tech Science Press, 2004.
[9] S. Lentzen, R. Schmidt: A geometrically nonlinear finite element for
transient analysis of piezolaminated shells, Proceedings Fifth
EUROMECH Nonlinear Dynamics Conference, Eindhoven, The
Netherlands, 7 - 12 August 2005, eds. D.H. van Campen, M.D. Lazurko,
W.P.J.M. van den Oever, 2492 - 2500, Eindhoven University of
Technology 2005.
[10] S. Lentzen, P. Klosowski, R. Schmidt: Geometrically nonlinear finite
element simulation of smart piezolaminated plates and shells, Smart
Mater. Struct.16 (2007), 2265-2274.
[11] T.D. Vu, S. Lentzen, R. Schmidt: Geometrically nonlinear FE-analysis
of piezolaminated plates based on first- and third-order shear
deformation theory, Proc. 8th International Conference on Mechatronics
Technology, ICMT 2004, Hanoi, Vietnam, 8 - 12 November 2004, eds.
Nguyen Khoa Son, Pham Thuong Cat, Pham Anh Tuan, 267-272,
Vietnam National University Publisher, Hanoi 2004.
[12] T.D. Vu, R. Schmidt: Nonlinear third-order shear deformation FE
simulation of the sensor output voltage of piezolaminated plates, in:
"Advances in Computational & Experimental Engineering and Science",
eds. W.H. Chen, S.N. Atluri, 452-458, Tech Science Press, Encino,
California, USA, 2009.
[13] R. Schmidt, T.D. Vu : Nonlinear dynamic FE simulation of smart
piezolaminated structures based on first- and third-order transverse shear
deformation theory, Advanced Materials Research, 79-82 (2009), 1313-
1316.
[14] T. Bailey, J.E. Hubbard: Distributed piezoelectric-polymer active
vibration control of a cantilever beam, AIAA J. of Guidance, Control,
and Dynamics 8 (1985), 605-611.
[15] I. Kreja, R. Schmidt: Large rotations in first-order shear deformation FE
analysis of laminated shells, International Journal of Non-Linear
Mechanics 41 (2006), 101-123.
[16] R. Schmidt, J.N. Reddy: A refined small strain and moderate rotation
theory of elastic anisotropic shells, ASME Journal of Applied Mechanics
55 (1988), 611-617.
[17] I. Kreja, R. Schmidt, J.N. Reddy: Finite elements based on a first-order
shear deformation moderate rotation shell theory with applications to the
analysis of composite structures, Int. J. of Non-Linear Mechanics 32
(1997), 1123-1142.
[18] Q.D. Nguyen, S. Lentzen, R. Schmidt: A geometrically nonlinear thirdorder
shear deformation finite plate element incorporating piezoelectric
layers, Proc. 8th International Conference on Mechatronics Technology,
ICMT 2004, Hanoi, Vietnam, 8 - 12 November 2004, eds. Nguyen Khoa
Son, Pham Thuong Cat, Pham Anh Tuan, 303-308, Vietnam National
University Publisher, Hanoi 2004.
[19] I. Kreja, R. Schmidt, Moderate rotation shell theory in FEM application.
Zeszyty Naukowe Politechniki Gdańskiej (Research Transactions of
Gdansk University of Technology), 522 (1995), 229-249.
[1] E.F. Crawley, J. de Luis: Use of piezoelectric actuators as elements of
intelligent structures, AIAA Journal 25 (1987), 1373-1385.
[2] R. Lammering: The application of finite shell elements for composites
containing piezoelectric polymers in vibration control, Computers &
Structures 41 (1991), 1101-1109.
[3] H. Kioua, S. Mirza: Piezoelectric induced bending and twisting of
laminated composite shallow shells, Smart. Mater. Struct. 6 (2000), 476-
484.
[4] S. Lee, N.S. Goo, H.C. Park, K.J. Yoon, C. Cho: A nine-node assumed
strain shell element for analysis of a coupled electromechanical system,
Smart. Mater. Struct. 12 (2003), 355-336.
[5] Chr├│ścielewski, P. Klosowski, R. Schmidt: Theory and numerical
simulation of nonlinear vibration control of arches with piezoelectric
distributed actuators, Machine Dynamics Problems 20 (1998), 73-90.
[6] S. Yi, S.F. Ling, M. Ying: Large deformation finite element analyses of
composite structures integrated with piezoelectric sensors and actuators,
Finite Elements in Analysis and Design 35 (2000), 1-15.
[7] A. Mukherjee, A.S. Chaudhuri: Piezolaminated beams with large
deformations, Int. J. of Solids and Structures 14 (2002), 1567-1582.
[8] S. Lentzen, R. Schmidt: Simulation of sensor application and shape
control of piezoelectric structures at large deflections, in Advances in
Computational & Experimental Engineering & Science, eds. S.N. Atluri,
A.J.B Tadeu, p. 439-444, Tech Science Press, 2004.
[9] S. Lentzen, R. Schmidt: A geometrically nonlinear finite element for
transient analysis of piezolaminated shells, Proceedings Fifth
EUROMECH Nonlinear Dynamics Conference, Eindhoven, The
Netherlands, 7 - 12 August 2005, eds. D.H. van Campen, M.D. Lazurko,
W.P.J.M. van den Oever, 2492 - 2500, Eindhoven University of
Technology 2005.
[10] S. Lentzen, P. Klosowski, R. Schmidt: Geometrically nonlinear finite
element simulation of smart piezolaminated plates and shells, Smart
Mater. Struct.16 (2007), 2265-2274.
[11] T.D. Vu, S. Lentzen, R. Schmidt: Geometrically nonlinear FE-analysis
of piezolaminated plates based on first- and third-order shear
deformation theory, Proc. 8th International Conference on Mechatronics
Technology, ICMT 2004, Hanoi, Vietnam, 8 - 12 November 2004, eds.
Nguyen Khoa Son, Pham Thuong Cat, Pham Anh Tuan, 267-272,
Vietnam National University Publisher, Hanoi 2004.
[12] T.D. Vu, R. Schmidt: Nonlinear third-order shear deformation FE
simulation of the sensor output voltage of piezolaminated plates, in:
"Advances in Computational & Experimental Engineering and Science",
eds. W.H. Chen, S.N. Atluri, 452-458, Tech Science Press, Encino,
California, USA, 2009.
[13] R. Schmidt, T.D. Vu : Nonlinear dynamic FE simulation of smart
piezolaminated structures based on first- and third-order transverse shear
deformation theory, Advanced Materials Research, 79-82 (2009), 1313-
1316.
[14] T. Bailey, J.E. Hubbard: Distributed piezoelectric-polymer active
vibration control of a cantilever beam, AIAA J. of Guidance, Control,
and Dynamics 8 (1985), 605-611.
[15] I. Kreja, R. Schmidt: Large rotations in first-order shear deformation FE
analysis of laminated shells, International Journal of Non-Linear
Mechanics 41 (2006), 101-123.
[16] R. Schmidt, J.N. Reddy: A refined small strain and moderate rotation
theory of elastic anisotropic shells, ASME Journal of Applied Mechanics
55 (1988), 611-617.
[17] I. Kreja, R. Schmidt, J.N. Reddy: Finite elements based on a first-order
shear deformation moderate rotation shell theory with applications to the
analysis of composite structures, Int. J. of Non-Linear Mechanics 32
(1997), 1123-1142.
[18] Q.D. Nguyen, S. Lentzen, R. Schmidt: A geometrically nonlinear thirdorder
shear deformation finite plate element incorporating piezoelectric
layers, Proc. 8th International Conference on Mechatronics Technology,
ICMT 2004, Hanoi, Vietnam, 8 - 12 November 2004, eds. Nguyen Khoa
Son, Pham Thuong Cat, Pham Anh Tuan, 303-308, Vietnam National
University Publisher, Hanoi 2004.
[19] I. Kreja, R. Schmidt, Moderate rotation shell theory in FEM application.
Zeszyty Naukowe Politechniki Gdańskiej (Research Transactions of
Gdansk University of Technology), 522 (1995), 229-249.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:64371", author = "Ruediger Schmidt and Thang Duy Vu", title = "Comparative Finite Element Simulation of Nonlinear Vibrations and Sensor Output Voltage of Smart Piezolaminated Structures", abstract = "Two geometrically nonlinear plate theories, based either on first- or third-order transverse shear deformation theory are used for finite element modeling and simulation of the transient response of smart structures incorporating piezoelectric layers. In particular the time histories of nonlinear vibrations and sensor voltage output of a thin beam with a piezoelectric patch bonded to the surface due to an applied step force are studied.
", keywords = "Nonlinear vibrations, piezoelectric patches, sensor voltage output, smart structures.", volume = "4", number = "3", pages = "342-4", }
